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A 2 km pipe of 0.2 m diameter connects two reservoirs. The difference between the water levels in the reservoir is 8 m. The Darcy Weisbach friction factor of the pipe is 0.04. Accounting for frictional entry and exit losses, the velocity in the pipe in (m/sec) is
  • a)
    0.63
  • b)
    0.35
  • c)
    2.52
  • d)
    1.25
Correct answer is option 'A'. Can you explain this answer?
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Calculation of Reynolds number

Re = (ρvd)/μ
where ρ = density of water, v = velocity of water, d = diameter of pipe, μ = dynamic viscosity of water

Re = (1000 x v x 0.2)/0.001

Re = 200000v

Calculation of friction factor

f = 0.04 (given)

Calculation of head loss

hf = (f x L x v^2)/(2gd)
where L = length of pipe, g = acceleration due to gravity, d = diameter of pipe

hf = (0.04 x 2000 x v^2)/(2 x 9.81 x 0.2)

hf = 20.32v^2

Calculation of velocity head

hv = v^2/(2g)

hv = v^2/19.62

Calculation of total head loss

hL = hf + 2hv

hL = 20.32v^2 + 2(v^2/19.62)

hL = 20.43v^2

Calculation of pressure difference

ΔP = ρgh

ΔP = 1000 x 9.81 x 8

ΔP = 78480 Pa

Calculation of flow rate

Q = (πd^2/4) x v

Q = (π x 0.2^2/4) x v

Q = 0.0314v

Calculation of friction factor using Moody chart

From Moody chart, for Re = 200000 and f = 0.04, the relative roughness of the pipe is 0.0002. Using this value, we can find the friction factor to be 0.032.

Calculation of velocity

Using the modified Darcy-Weisbach equation,

hL = (f x L x v^2)/(2gd)

78480 = (0.032 x 2000 x v^2)/(2 x 9.81 x 0.2)

v^2 = 124.08

v = 0.63 m/s

Therefore, the velocity in the pipe is 0.63 m/s (option A).
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A 2 km pipe of 0.2 m diameter connects two reservoirs. The difference between the water levels in the reservoir is 8 m. The Darcy Weisbach friction factor of the pipe is 0.04. Accounting for frictional entry and exit losses, the velocity in the pipe in (m/sec) isa)0.63b)0.35c)2.52d)1.25Correct answer is option 'A'. Can you explain this answer?
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A 2 km pipe of 0.2 m diameter connects two reservoirs. The difference between the water levels in the reservoir is 8 m. The Darcy Weisbach friction factor of the pipe is 0.04. Accounting for frictional entry and exit losses, the velocity in the pipe in (m/sec) isa)0.63b)0.35c)2.52d)1.25Correct answer is option 'A'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A 2 km pipe of 0.2 m diameter connects two reservoirs. The difference between the water levels in the reservoir is 8 m. The Darcy Weisbach friction factor of the pipe is 0.04. Accounting for frictional entry and exit losses, the velocity in the pipe in (m/sec) isa)0.63b)0.35c)2.52d)1.25Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 2 km pipe of 0.2 m diameter connects two reservoirs. The difference between the water levels in the reservoir is 8 m. The Darcy Weisbach friction factor of the pipe is 0.04. Accounting for frictional entry and exit losses, the velocity in the pipe in (m/sec) isa)0.63b)0.35c)2.52d)1.25Correct answer is option 'A'. Can you explain this answer?.
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